TWI582545B - Lithographic apparatus and method - Google Patents

Description

Micro-shadow device and method

The present invention relates to a lithography apparatus and a method of fabricating the same.

A lithography apparatus is a machine that applies a desired pattern to a target portion of a substrate. The lithography apparatus can be used, for example, in the fabrication of integrated circuits (ICs). In that case, a patterned device (which is alternatively referred to as a photomask or a proportional mask) can be used to create a circuit pattern corresponding to individual layers of the IC, and this pattern can be imaged to have a radiation sensitive material (resist A target portion (for example, a portion including a crystal grain, a crystal grain or a plurality of crystal grains) on a substrate (for example, a germanium wafer) of a layer. In general, a single substrate will contain a network of adjacent target portions that are sequentially exposed. It is known that lithography apparatus includes a so-called scanner in which each target portion is irradiated by scanning a pattern through a beam in a given direction ("scanning" direction) while simultaneously scanning the substrate in parallel or anti-parallel to this direction.

There is a need to provide a lithography apparatus that allows us to accurately control the dose of radiation received by each point on the target portion of the substrate. The dose of radiation received by a portion of the target area of the substrate can be defined as the amount of energy received by the portion per unit area. The precise control of the dose of radiation in turn allows control of variations in the critical dimensions of the features formed on the substrate.

It is an object of the present invention to provide a lithography apparatus and device fabrication method that at least partially processes one or more of the prior art problems identified herein or elsewhere.

According to an aspect of the present invention, a lithography apparatus is provided, comprising: a radiation system operable to generate a radiation beam; a frame; a substrate stage for holding a substrate, the substrate stage being movably Mounted to the frame and configured such that a target portion of the substrate is configured to receive the radiation beam; a scanning mechanism operative to move the substrate table relative to the frame; and a mechanism operable to determine an indication a quantity of the radiation system relative to one of the speeds of the frame; wherein the radiation system is provided with an adjustment mechanism operable to control the radiation beam depending on the number indicative of the speed of the radiation system relative to the frame One of the powers to reduce a change in one of the doses of radiation received by the substrate caused by the relative motion of the radiation system and the frame.

The radiation beam can be projected onto the target portion of the substrate as a radiation strip, and by moving the substrate stage, the lithography apparatus is operable to move the substrate relative to the radiation strip. During scanning exposure, the dose of radiation delivered to a point on the substrate is given by the time integral of the irradiance of the radiation beam to the other point. Thus, the dose of radiation received by a given point on the substrate depends on the speed at which the radiation strip moves over the surface of the substrate. For example, if the power of the radiation beam remains constant, the lower the rate at which the radiation strip moves over the surface of the substrate, the greater the dose of radiation.

Any relative movement of the radiation system to the frame will affect the rate at which the radiation belt moves over the surface of the substrate, and thus the dose of radiation received by the substrate. For example, the radiation system can be loosely mechanically coupled to the frame such that movement of the substrate table relative to the frame by the scanning mechanism can cause the radiation system to vibrate relative to the frame. Any such vibration in the direction of movement of the substrate table relative to the frame will cause the velocity of the radiation band to move over the surface of the substrate to oscillate over time, and thus the radiation dose received by the substrate will oscillate over time. This first aspect of the invention allows for at least partially compensating for this variation in the dose received by the substrate by varying the power of the radiation beam.

In general, it is desirable to have an accurate control of the dose of radiation received by each point on the substrate, which is defined as the amount of energy received by the substrate per unit area. Example In particular, it may be desirable to control the dose sufficiently accurately that the change in the critical dimension of the features formed on the substrate is below the desired threshold.

The mechanism operable to determine the amount indicative of one of the speeds of the radiation system relative to the frame can include an accelerometer mounted on the radiation system. The mechanism operable to determine the amount indicative of one of the speeds of the radiation system relative to the frame can include a plurality of accelerometers mounted on the radiation system or both the radiation system and the frame.

The mechanism operable to determine the amount indicative of one of the speeds of the radiation system relative to the frame can include a camera mounted to the frame, the camera operable to measure the movement of the radiation band of one of the radiation systems. The mechanism operable to determine an amount indicative of one of the speeds of the radiation system relative to the frame can include a plurality of cameras mounted on the frame, the plurality of cameras operable to measure a radiation band of the radiation system Move.

The adjustment mechanism is operable to control the power of the radiation beam such that it is equal to a base power multiplied by a factor that depends on the amount indicative of the speed of the radiation system relative to the frame. The base power may be one of the doses required to achieve one of the radiations when the radiation system is stationary relative to the frame. This factor can vary over time. The base power can be substantially time independent. Alternatively, the base power can vary over time. For example, the base power can be varied to at least partially compensate for one or more time dependent changes within the lithography apparatus.

The factor may be proportional to a vector sum of one of the substrate stages relative to the frame and a vector sum of one of the speeds of the radiation beam in the scanning direction relative to the frame in the plane of the substrate. The factor can be the ratio of the sum to the scanning speed of the substrate table relative to the frame. The velocity of the radiation beam relative to the frame in the plane of the substrate in a scanning direction is given by the speed of the radiation system relative to the frame divided by a reduction factor applied to the radiation The radiation beam between the system and the plane of the substrate.

This factor can include one or more tunable parameters. For example, the factor may be proportional to a vector sum of one of: a substrate scanning speed relative to one of the frames; and a parameter f and the radiation beam in the scanning direction in the plane of the substrate The product of one of the speeds relative to the frame. The factor can be the ratio of the sum to the scanning speed of the substrate table relative to the frame.

The radiation system can include a radiation source operable to generate a radiation beam and an illumination system operable to adjust the radiation beam.

The radiation system can include an exit slot. The exit slot can form part of the illumination system. The exit slot can be provided with one or more movable adjustable fingers. The exit slot can further comprise two movable vanes. Each vane is moveable between at least a position at which it at least partially shields the slit and a position where it does not obscure the slit. Each blade can be moved to a position where it completely obscures the slot.

The lithography apparatus can further include a support structure for supporting a patterned device. The radiation system can be configured to project the radiation beam onto the patterned device such that the patterned device imparts to the radiation beam in a cross section of the radiation beam before the radiation beam is received by the target portion of the substrate a pattern. The support structure is movably mounted to the frame, and the scanning mechanism is further operable to move the support structure relative to the frame.

The lithography apparatus can further include a projection system for projecting the radiation beam as a radiation strip onto the target portion of the substrate. The projection system can be connected to the frame.

The radiation system can include a laser. The laser can be a quasi-molecular laser.

According to a second aspect of the present invention, a method is provided, comprising: providing a substrate; providing a radiation beam using a radiation system; and using a patterned device to impart a radiation beam to the radiation beam in a cross section of the radiation beam a pattern; projecting the patterned radiation beam onto a target portion of the substrate; using a scanning mechanism to move relative to a frame The substrate causes the patterned radiation beam to move over a surface of the substrate; determining a quantity indicative of one of the speeds of the radiation system relative to the frame; and controlling a power of the radiation beam such that it depends on the indication of the radiation system The amount of velocity relative to one of the frames is such as to reduce one of the doses of one of the radiation received by the substrate caused by the relative motion of the radiation system and the frame.

Various aspects and features of the inventions set forth above or below may be combined with various other aspects and features of the invention as will be readily apparent to those skilled in the art.

100‧‧‧Partial transmission mirror

101‧‧‧The first part of the radiation beam

102‧‧‧The remainder of the radiation beam

210‧‧‧First curve

211‧‧‧ periodic maximum

212‧‧‧min

220‧‧‧second curve

221‧‧‧Periodic maximum

222‧‧‧min

230‧‧‧ third curve

231‧‧‧Periodic maximum

232‧‧‧min

310‧‧‧First curve

320‧‧‧second curve

330‧‧‧ third curve

AC‧‧ ‧ accelerometer

AM‧‧‧Adjustment components

BD‧‧•beam delivery system

BF‧‧ pedestal frame

C‧‧‧Target section

CN‧‧‧Controller

CO‧‧‧ concentrator

DM‧‧‧Acoustic Damping Mount

IF‧‧‧ position sensor

IL‧‧‧Lighting system/illuminator

IN‧‧‧ concentrator

M1‧‧‧ patterned device alignment mark

M2‧‧‧ patterned device alignment mark

MA‧‧‧patterned device

MF‧‧‧Isolated framework

MT‧‧‧Support structure/object table

P1‧‧‧ substrate alignment mark

P2‧‧‧ substrate alignment mark

PB‧‧‧radiation beam

PL‧‧‧Projection System

PM‧‧‧First Positioning Device

PW‧‧‧Second positioning device

RS‧‧‧radiation sensor

SL‧‧‧ slit

SO‧‧‧pulse source

W‧‧‧Substrate

WT‧‧‧Substrate/object table

Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which FIG. a lithography apparatus of one embodiment; - Figure 2 shows the variation of the vibration frequency with respect to the first intensity distribution caused by the vibration of the illuminator relative to the frame (in the scanning direction) as the fingers of the illuminator contract A graph of the simulation of the three sigma dose changes (in units of reduction); - Figure 3 shows an enlarged section of the graph of Figure 2, which is shown on a smaller frequency scale; and - Figure 4 shows the fingers in the illuminator A plot of the simulation of the tristimulus dose change (in units of reduction) as a function of the vibration frequency of the second intensity distribution caused by the vibration of the illuminator relative to the frame when the piece is partially inserted.

Although reference may be made specifically to the use of lithography apparatus in IC fabrication herein, it should be understood that the lithographic apparatus described herein may have other applications, such as manufacturing integrated optical systems, for magnetic domain memory. Lead to detection patterns, liquid crystal displays (LCDs), thin film heads, and more. Those skilled in the art should understand that in the context of the content of such alternative applications, any use of the terms "wafer" or "die" herein is considered synonymous with the more general term "substrate" or "target portion". . Can be before or after exposure (for example) The substrates referred to herein are treated in a coating development system (usually a resist layer is applied to the substrate and the exposed resist is developed) or a metrology or inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Additionally, the substrate can be processed more than once, for example, to create a multilayer IC, such that the term "substrate" as used herein may also refer to a substrate that already contains multiple processed layers.

The terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (for example, having 365 nm, 248 nm, 193 nm, 157 nm or 126 nm). Wavelengths) and extreme ultraviolet (EUV) radiation (eg, having a wavelength in the range of 5 nm to 20 nm); and particle beams (such as ion beams or electron beams).

The term "patterned device" as used herein shall be interpreted broadly to mean a device that can be used to impart a pattern to a radiation beam in a cross-section of a radiation beam to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device (such as an integrated circuit) produced in the target portion.

The patterned device can be transmissive or reflective. Examples of patterned devices include photomasks, programmable mirror arrays, and programmable LCD panels. Photomasks are well known in lithography and include reticle types such as binary, alternating phase shift and attenuated phase shift, as well as various hybrid mask types. One example of a programmable mirror array uses a matrix configuration of small mirrors, each of which can be individually tilted to reflect an incident radiation beam in different directions; in this manner, the reflected beam is patterned.

The support structure holds the patterned device. The support structure holds the patterned device in a manner that depends on the orientation of the patterned device, the design of the lithographic device, and other conditions, such as whether the patterned device is held in a vacuum environment. The support can use mechanical clamping, vacuum or other clamping techniques, such as electrostatic clamping under vacuum conditions. The support structure can be For example, a frame or table that can be fixed or movable as needed and that ensures that the patterned device is, for example, in a desired position relative to the projection system. Any use of the terms "proportional mask" or "reticle" herein is considered synonymous with the more general term "patterned device."

The term "projection system" as used herein shall be interpreted broadly to encompass various types of projection systems suitable for, for example, exposure radiation used or other factors suitable for use such as the use of infiltrating fluids or the use of vacuum, including Refractive optical systems, reflective optical systems, and catadioptric optical systems. Any use of the term "projection lens" herein is considered synonymous with the more general term "projection system."

The illumination system can also encompass various types of optical components, including refractive, reflective, and catadioptric optical components for guiding, shaping, or controlling the radiation beam, and such components can also be collectively or individually referred to as "lenses" hereinafter. "."

The lithography apparatus can have a single substrate stage and a single support structure. Alternatively, the lithography apparatus may be of the type having two (dual stage) or more than two substrate stages (and/or two or more support structures). In such "multi-stage" machines, additional stations may be used in parallel, or one or more stations may be subjected to preliminary steps while one or more other stations are used for exposure.

The lithography apparatus can also be of the type wherein the substrate is immersed in a liquid (eg, water) having a relatively high refractive index to fill the space between the final element of the projection system and the substrate. Infiltration techniques are well known in the art for increasing the numerical aperture of a projection system.

Figure 1 schematically depicts a lithography apparatus in accordance with a particular embodiment of the present invention. The apparatus comprises: - a lighting system (illuminator) IL for adjusting the radiation beam PB (for example, UV radiation or DUV radiation); - a frame MF; - a base frame BF; - a support structure (for example, a reticle stage) MT, which is used to support patterned devices (eg, Photomask) MA; - a substrate stage (eg, wafer table) WT for holding a substrate (eg, a resist coated wafer) W; and - a projection system (eg, a refractive projection lens) PL, The configuration is to image a pattern imparted by the patterned device MA to the radiation beam PB onto a target portion C (eg, comprising one or more dies) of the substrate W.

The base frame BF can be supported on the ground. The frame MF is a vibration-isolated frame that is substantially isolated from external influences (such as vibrations in the base frame BF) by using an acoustic damping mount DM that supports the frame MF to the base frame BF. These acoustic damping mounts DM can be actively controlled to be isolated from vibrations introduced by the base frame BF and/or by the isolation frame MF itself.

The projection system PL is connected to the isolated frame MF. The support structure MT is movably mounted to the frame MF via the first positioning device PM. The first positioning device PM can be used to move the patterned device MA and accurately position the patterned device MA relative to the frame MF (and the projection system PL connected to the frame MF). The substrate stage WT is movably mounted to the frame MF via the second positioning device PW. The second positioning device PW can be used to move the substrate W and accurately position the substrate W with respect to the frame MF (and the projection system PL connected to the frame MF). The second positioning device PW may be referred to as a scanning mechanism. Alternatively, the first positioning device PM and the second positioning device PW may be collectively referred to as a scanning mechanism. The support structure MT and the substrate table WT may be collectively referred to as an object table.

As depicted herein, the device is of a transmissive type (eg, using a transmissive reticle). Alternatively, the device may be of a reflective type (eg, using a programmable mirror array of the type mentioned above).

The illuminator IL receives a radiation beam from the radiation source SO. For example, when the radiation source SO is a quasi-molecular laser, the radiation source SO and the lithography apparatus may be separate entities. Under these conditions, the radiation source is not considered to form part of the lithography apparatus, and the radiation beam is based on inclusion (eg For example, a beam delivery system BD that is directed to the mirror and/or beam expander is passed from the radiation source SO to the illuminator IL. In other cases, for example, when the source of radiation is a mercury lamp, the source of radiation can be an integral part of the device. The illuminator IL can be referred to as a radiation system. Alternatively, the radiation source SO and the illuminator IL together with the beam delivery system BD may be collectively referred to as a radiation system as needed.

The illuminator IL may comprise an adjustment member AM for adjusting the angular intensity distribution of the light beam. In general, at least the outer radial extent and/or the inner radial extent (commonly referred to as σ outer and σ inner, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. In addition, the illuminator IL typically includes various other components such as the concentrator IN and the concentrator CO.

The shape and intensity distribution of the modulated radiation beam PB is defined by the optics of the illuminator IL. The illuminator IL comprises a slit SL through which the modulated radiation beam PB passes. The slit SL comprises an elongate generally rectangular aperture defined by a plurality of movable fingers. The slits may have a longer dimension (which may be referred to as the length of the slit) and a shorter dimension (which may be referred to as the width of the slit). Each movable finger is independently movable between at least one retracted position in which it is not disposed in the path of the radiation beam and an inserted position that partially blocks the radiation beam. The shape and/or intensity distribution of the slit SL can be adjusted by moving the fingers. The finger is not in the field plane and the field will be in the penumbra of the finger. Therefore, the fingers do not sharply cut off the radiation beam PB. The movement of the finger between its retracted position and the inserted position may be in a direction perpendicular to the length of the slit SL. The fingers can be arranged in pairs, each pair comprising a finger on each side of the slot SL. The pair of fingers can be configured along the length of the slot SL. The pair of fingers can be used to apply different levels of attenuation of the radiation beam PB along the length of the slot SL.

The intensity distribution of the radiation beam PB may depend on the location of the plurality of fingers (and the optics of the illuminator IL). The intensity function of the radiation beam PB can vary across the width of the slit SL corresponding to the scanning direction. The shape of the intensity function across the width of the slit SL may be referred to as the contour of the radiation beam PB. The profile of the radiation beam PB can be substantially phased along the length of the slot SL with. Additionally or alternatively, the intensity profile of the radiation beam PB across the width of the slot SL may be substantially constant along the length of the slot SL. This can be achieved by inserting the pairs of fingers into the path of the radiation beam PB in different amounts to attenuate the radiation beam along the length of the slot SL by a different amount. For such embodiments in which the pairs of fingers are inserted into the path of the radiation beam PB by different amounts, the profile of the radiation beam PB will vary slightly along the length of the slot SL.

The illuminator IL comprises two blades (not shown). Each of the two vanes is substantially parallel to the length of the slot SL, the two vanes being disposed on opposite sides of the slot. Each vane is independently movable between a retracted position in which it is not disposed in the path of the radiation beam and an inserted position that partially blocks the radiation beam. By moving the blade into the path of the radiation beam, the profile of the radiation beam PB can be truncated, thus limiting the extent of the field of the radiation beam PB in the scanning direction.

The illuminator IL provides an conditioned radiation beam PB having a desired uniformity and intensity distribution in cross section.

The radiation beam PB exiting the slit SL of the illuminator IL is incident on a patterned device (e.g., reticle) MA that is held on the support structure MT. In the case where the patterned device MA has been traversed, the light beam PB is transmitted through the projection system PL, and the projection system PL focuses the light beam onto the target portion C of the substrate W. With the second positioning device PW and the position sensor IF (for example, an interference measuring device), the substrate table WT can be accurately moved relative to the frame MF, for example, to position the different target portions C in the path of the light beam PB. . Similarly, the first positioning device PM and another position sensor (which is not explicitly depicted in Figure 1) can be used, for example, after mechanical extraction from the reticle library or during scanning relative to the frame MF To accurately position the patterned device MA. In general, the movement of the object table MT and WT will be achieved by means of a long stroke module (rough positioning) and a short stroke module (fine positioning) forming the components of the positioning device PM and PW. The patterned device MA and the substrate W can be aligned using the patterned device alignment marks M1, M2 and the substrate alignment marks P1, P2.

The projection system PS can apply a reduction factor to the radiation beam PB to form an image having features that are less than the corresponding features on the patterned device MA. For example, a reduction factor of 4 can be applied.

The depicted device can be used in scan mode. In the scan mode, when the pattern to be given to the light beam PB is projected onto the target portion C, the support structure MT and the substrate stage WT (i.e., single-shot dynamic exposure) are synchronously scanned. In some embodiments, the support structure MT and the substrate table WT are scanned in opposite directions. The speed and direction of the substrate stage WT relative to the support structure MT can be determined by the magnification (reduction ratio) and image inversion characteristics of the projection system PL. For example, for embodiments in which the projection system PS is applied as a reduction factor of N, the rate of the support structure MT can be greater than the rate of the substrate table WT by a factor of N. In the scan mode, the maximum size of the exposure field limits the width of the target portion in a single dynamic exposure (in the non-scanning direction), and the length of the scanning motion determines the height of the target portion (in the scanning direction).

In the scan mode, the projection system PL focuses the radiation beam (as a radiation strip) at the exposure zone in the plane of the substrate W. The blades of the illuminator IL can be used to control the width of the radiation zone within the exposure zone. At the beginning of a single dynamic exposure of the target portion C, the first of the blades of the slit SL can be placed in the path of the radiation beam to act as a light shield such that portions of the exposure region do not receive radiation. When the edge is moved into the exposure zone before the target portion C of the substrate, the first blade is moved such that only a portion of the target region C disposed in the exposure region receives radiation (i.e., a portion of the substrate outside the target region is not exposed). Through the exposure of the target portion C midway, both of the blades can contract from the path of the radiation beam such that the entire exposure region receives radiation. When the edge is removed from the exposed area before the target portion C of the substrate, the second vanes of the vanes move such that only a portion of the target area C disposed in the exposed area receives radiation.

Alternatively, the depicted device can be used in another mode in which the support structure MT is held substantially stationary while the pattern imparted to the beam PB is projected onto the target portion C, thereby holding the programmable patterning device and moving Or scan the substrate table WT. In this mode, a pulsed radiation source is typically used and after each movement of the substrate table WT or in one The programmable patterning device is updated as needed between successive pulses of radiation during the scan. This mode of operation can be readily applied to matte lithography utilizing a programmable patterning device such as a programmable mirror array of the type mentioned above.

Combinations and/or variations or completely different modes of use of the modes of use described above may also be used.

The radiation source SO delivers the radiation to the lithography apparatus for projection onto the substrate W as a radiation strip. With the MF with respect to the frame (and the projection system PL) movement of the substrate table WT, lithography apparatus operable with radiation with respect to a scanning movement of the substrate W. velocity v ₀ It should be noted that for embodiments in which the projection system PS applies a reduction factor to the radiation beam, the patterned device MA will move at different speeds relative to the radiation band. During exposure, the lithography apparatus is operable to move the substrate W a fixed distance relative to the radiation strip. By performing this movement, the lithography apparatus is therefore operable to expose the target portion C of the substantially fixed area to radiation. For example, the target portion C may comprise a portion of a die, a die or a plurality of grains. After exposure of the first target portion C, the lithography apparatus can be further operable to move the substrate W relative to the projection system PL such that the second target portion C can be exposed to radiation. A single wafer can be exposed to radiation in a number of steps, each step involving exposure of target portion C, followed by movement of substrate W.

In general, it is desirable to have an accurate control of the dose of radiation received by each point on the substrate W, which is defined as the amount of energy received by the substrate W per unit area. It may be desirable to control the dose sufficiently accurately that the change in the critical dimension of the features formed on the substrate W is below the desired threshold.

During scanning exposure, the radiation dose E(r) delivered to the point on the substrate W (at position r ) is given by the time integral I ( r , t ) of the irradiance for the radiation of the other point: Where t ₁ is the time before the edge of the radiation band passes through the position r , and t ₂ is the time after the edge of the radiation band passes the position r . The irradiance is the power received by the substrate W per unit area.

If the irradiance is assumed to be constant, the dose received by a given point on the substrate W is proportional to the time (t _{2 -} t ₁ ) it takes for the radiation band to pass through the point. The time it takes for the radiation band to pass through a given point is given by the ratio of the magnitude of the radiation band in the scanning direction to the velocity v of the radiation band moving over the substrate W. Thus, the dose received by a given point on the substrate W is inversely proportional to the velocity v of the radiation strip moving over the substrate W. For a first order approximation, the radiation zone of the substrate W is moved upward based speed v (i.e., the substrate table WT relative to the frame MF) is given by the scanning velocity v _0.

During operation in the scan mode, the first positioning device PM and the second positioning device PW are used to move the patterned device MA and the substrate W. In order to promote high yield lithography, the support structure MT and the substrate table WT may undergo rapid acceleration and deceleration, which in turn may exert a strong force on the susceptor frame BF supported via the isolation frame MF. These induced forces are partially compensated by the anti-movement balance mass, but this compensation is not perfect and, therefore, some residual force is applied to the base frame BF. The residual force on the base frame BF induces vibration of the base frame BF. Although the illuminator IL may not be directly mounted to the base frame BF, the illuminator IL is coupled to the base frame BF, and there is some physical coupling between the base frame BF and the illuminator IL. Therefore, the vibration of the base frame BF is transmitted to the illuminator IL (and other components directly or indirectly coupled to the base frame BF) to some extent. This situation causes vibrations of the illuminator IL, which are generally in all directions and in particular in the scanning direction. These vibrations of the illuminator IL in the scanning direction cause a vibrational radiation band on the patterned device MA and the substrate W. These vibrations can be considered to modulate the velocity v of the radiation strip across the patterned device MA and the substrate W sweep. Therefore, the dose of the radiation received by the substrate W is modulated by vibration.

The amplitude of the vibration of the illuminator IL depends on: the movement performed by the support structure MT and the substrate table WT; and the coupling between the illuminator IL and the base frame BF. For example, the amplitude of the vibration of the illuminator IL can be about 10 microns. If the projection system PS applies a reduction factor of 4 to the radiation beam, this corresponds to a vibration of the radiation band projected onto the substrate W having an amplitude of about 2.5 microns. If uncorrected, this can cause a difference from the substrate W. Significant changes in the amount of radiation received.

Embodiments of the invention are provided with: (a) a mechanism operable to determine a quantity indicative of a speed of the illuminator IL relative to the frame MF; and (b) an adjustment mechanism operable to depend on the indication radiation system relative to The power of the radiation beam PB varies by the amount of velocity of the frame to at least partially compensate for any change in the dose of radiation received by the substrate W caused by the relative motion of the illuminator IL and the frame MF.

Embodiments of mechanisms operable to determine the number of speeds indicative of illuminator IL relative to frame MF are now described. The accelerometer AC is mounted on the illuminator IL. The accelerometer AC can be mounted close to the slot SL of the illuminator IL. The accelerometer AC is operable to measure the acceleration of the illuminator IL relative to the frame MF in the scanning direction. The measured acceleration is integrated over the resolution time to calculate the instantaneous average velocity of the slot SL in the scan direction during the resolution time.

In Figure 1, the accelerometer AC is operable to measure the acceleration of the illuminator IL relative to the reference coordinates of the earth. In some embodiments, a second accelerometer (not shown) can be mounted on the frame MF, the second accelerometer being operative to measure the acceleration of the frame MF relative to the reference coordinates of the earth. In combination, an accelerometer AC mounted on the illuminator IL and an accelerometer mounted on the isolation frame MF can be used to determine the acceleration of the illuminator IL relative to the frame MF (in the scanning direction). However, as discussed above, in order to perform precision lithography, the frame MF is likely to be mechanically well insulated from its environment by means of the acoustic damping mount DM, and therefore, the frame MF can be assumed to be stationary relative to the reference coordinates of the earth. Therefore, a single accelerometer AC can be used to determine the acceleration of the illuminator IL relative to the frame MF.

In one embodiment, the accelerometer AC includes three separate accelerometers, each mounted to a slot SL proximate to the illuminator IL. This situation allows the acceleration (and velocity) of the slot in the scanning direction (to the page in Figure 1) to be decomposed into: a component corresponding to the linear motion of the slot in the scanning direction; corresponding to the slot around the Z axis (see Figure 1) The component of the rotation; and the component of the rotation corresponding to the slot around the X axis (see Figure 1). Corresponding to the gap around The component of the rotation of the X-axis and the Z-axis does not contribute to the speed of the radiation band swept above the substrate W (but does affect the size of the exposed area) and is therefore discarded. Only the component corresponding to the linear motion of the slit in the scanning direction is used to determine how the power of the radiation beam PB should be modulated.

The accelerometer AC is operable to determine the acceleration of the illuminator IL relative to the frame MF in the scanning direction and to output a signal indicative thereof to the controller CN (shown in Figure 1). The controller CN can include a microprocessor. The controller CN can be configured to integrate the measured acceleration in the resolution time to calculate the average velocity v _s of the slot in the scan direction during the resolution time.

Alternatively, the accelerometer AC can be configured to integrate the measured acceleration in the resolution time to calculate the average velocity v _s of the slot in the scan direction during the resolution time. The accelerometer AC can be further operable to output a signal indicative of the average velocity v _s of the slot in the scan direction during the resolution time to the controller CN.

The controller CN is further configured to output a control signal to a radiation source SO (eg, a laser) that can be used to control one or more variables of the radiation source SO.

As discussed above, if the irradiation incident on the substrate W is assumed to be constant, the dose received by a given point on the substrate W is inversely proportional to the velocity v of the radiation band moving over the substrate W. Radiation with the upward movement of the substrate W by the train speed v and the scanning speed V ₀ is given to the radiation beam PB MF and the isolated frame and the substrate W in the plane of the instantaneous velocity of v _B of the (vector) in the scanning direction. If the reduction factor of the projection system does not apply, the radiation beam PB in the scanning direction with respect to the isolated frame MF and the speed v _b in the plane of the substrate W is equal to the velocity of the slit v _s. Application to the projection system PS embodiment of the reduction factor of N, the radiation beam PB is given by v _s / N in the scanning direction with respect to the isolated frame MF and the speed v _b line in the plane of the substrate W is in. Thus, in one embodiment of the invention, the controller is operative to output a control signal to a radiation source SO (eg, a laser) that controls the power of the radiation source SO according to the following equation: Where P (t) is the power of the radiation source, and P ₀ (t) is the case in the absence of any relative movement of the illuminator IL with the frame MF (i.e., where v _b = v _s = 0) to reach the radiation The basic power required for a given dose. For a continuous source of radiation, the power P ( t ) of the source can be a continuous function of time. Alternatively, for a pulsed radiation source, the power P ( t ) of the radiation source may comprise a plurality of time interval pulses. For a pulsed radiation source, according to equation (2) to select the energy of each pulse, where P (t) is the pulse energy at the time of time t, and P ₀ (t) as the illuminator IL, and the frame does not exist The basic pulse energy required to achieve a given dose of radiation in the event of any relative movement of the MF. It should be understood that the sum of the scanning speed v ₀ in equation (2) and the instantaneous velocity v _b ( t ) of the radiation beam is a vector sum. The scanning speed v ₀ is the speed of the substrate W (non-patterned device MA) relative to the frame MF. In general, the speed of the substrate W relative to the frame MF is different from the speed of the patterned device MA relative to the frame MF.

The rate at which the instantaneous velocity v _b (or equivalently, the velocity of the slit v _s ) of the radiation beam PB is determined should be higher than the typical frequency of the vibration of the illuminator IL relative to the frame MF. Due to the nature of the coupling between the illuminator IL and the frame MF, the frequency of any induced vibrations of the illuminator IL can be relatively low. For example, frequencies below 80 Hz may be excited only, and in some embodiments only frequencies below 30 Hz may be excited. The sampling rate of the accelerometer can be, for example, about 100 Hz to 200 Hz. A radiation source SO for generating pulsed radiation beam embodiment, the rate for determining the instantaneous velocity v _s of the slot without the high repetition rate of the radiation source SO, the repetition rate of the radiation source SO may be about several kilohertz. For the pulse of radiation generated between the two determinations of the velocity v _s of the slit by the accelerometer AC, interpolation or extrapolation can be used to estimate the velocity v _{s of the} slot.

Controlling the power of the radiation source according to equation (2) (or for the pulsed radiation source, the pulse energy of each of the control pulses) may be sufficient to cause the radiation received by the substrate W caused by the relative motion of the illuminator IL and the frame MF. Any change in dosage is reduced to an acceptable level. However, in general, the radiation incident on the substrate W may vary over time. The irradiance (see equation (1)) is the power received by the substrate W per unit area and is given by the following equation: I ( r , t ) = I _SO ( t ) × s ( r , t ) × m ( r ), (3) where I _SO ( t ) is the power density of the radiation beam; s ( r , t ) is a dimensionless distribution describing the spatial profile of the radiation band output by the illuminator IL; and m ( r ) is A dimensionless distribution of the pattern imparted to the radiation beam by the patterned device MA is indicated. In the following discussion, the contribution to the energy dose resulting from the pattern imparted to the radiation beam by the patterned device MA is ignored for the sake of simplicity. Therefore, in the following, the value of m is set to be at m =1.

The profile s ( r , t ) of the radiation zone is dependent on the optical components of the illuminator IL. In particular, it depends on the optics of the illuminator IL and the slit SL (as defined by a plurality of independently movable fingers). In general, the point r on the substrate W can be defined by two coordinates x , y . For example, the coordinate y can define the position of r in the scanning direction, and the coordinate x can describe the position of r in a direction substantially perpendicular to the scanning direction. Dimensionless value distribution s (r, t) may depend on the position in the scanning direction of the r (y), independently of the position and r is perpendicular to the scanning direction (x). For these embodiments, the profile of the radiation may be one-dimensional function f (y) is described, one-dimensional function f (y) at y = describe the general shape of the contour of the radiation in the scanning direction of the evaluation vt. The contour of the radiation strip in the scanning direction can have any convenient shape, such as a "top hat" shape, a trapezoidal shape, or a truncated Gaussian (or "Gaussian") shape.

It can be seen from Equation 1 that when there is no reticle MA (ie, m =1), the dose E (y) received by the point (position y ) on the substrate is dominated by the contour of the radiation band and the radiation source. The convolution of the power density is given.

The radiation source SO may be generated at a pulse frequency f _p pulsed radiation beam. For example, radiation source SO may comprise a laser generating a pulsed beam of pulses of radiation of frequency f _p (e.g., an excimer laser). For this configuration, the dose of radiation received by a given point on substrate W is the sum of the doses of radiation delivered by each pulse (all pulses throughout the given point of irradiation). Contribute to the dose for a given number of pulses depending on the point of the system: He sweep point band radiation through time spent; pulse frequency f _p; and a phase of a radiation pulse train prior to the edge profile through a given point, That is, the amount of time that passes between the leading edge of the contour and the first pulse at a given point to illuminate the given point. The time it takes for the radiation belt to sweep through a point is given by the ratio of the width of the radiation strip to the velocity v of the substrate W relative to the radiation movement.

For embodiments utilizing a pulsed radiation source SO, the power density of the radiation beam will depend on the pulse train of the radiation source. For example, I _SO ( t )= I ₀ ( t )× p ( t ), (5) where I ₀ ( t ) is the amplitude of the power density of the radiation source, and p ( t ) is a dimensionless pulse waveform . I ₀ ( t ) can be considered as the power density of an equivalent continuous radiation source, and the pulse waveform describes how this continuous radiation source is sampled at the pulse frequency f _p . Pulsed radiation can have any pulse train. The shape, duration and frequency of the pulse can be selected as needed or as needed. The pulse frequency can be, for example, about 6 KHz, which is equivalent to a pulse time period of about 0.17 milliseconds (although other pulse frequencies can be used). The duration of the pulse can be significantly less than the time period of the pulse train. For example, the ratio of the time period of the burst to the duration of the pulse can be about 1000 (or can be some other value). The duration of the pulse can be, for example, about 150 nanoseconds (although other pulse durations can be used).

In an embodiment of the invention, the controller CN is operative to output a control signal to a radiation source SO (eg, a laser) that depends on the relative velocity v _s of the illuminator IL and is different from the equation (2) The way to control the power of the radiation source (or the pulse energy of each of the pulses of the pulsed radiation source). In particular, it can be parameterized using a more accurate analysis of the radiation incident on the substrate W. For example, the controller CN is operative to output a control signal that controls the power of the radiation source to a radiation source SO (eg, a laser) according to the following equation:

Where f is a parameter that is close to but not equal to one. For example, f can be about 0.995.

The value of parameter f can be selected to optimize the reduction in dose variation on the surface of substrate W. The value of the parameter f may depend on the optics of the illuminator IL. In particular, the parameter f may depend on the shape of the intensity distribution in the pupil plane of the illuminator IL (for example, it may depend on the outer radial extent, inner diameter of the intensity distribution in the pupil plane of the illuminator IL) Range and / or range of angles). Additionally or alternatively, the parameter f may depend on the shape of the slot SL of the illuminator IL as defined by the position of the plurality of independently moveable fingers. Additionally or alternatively, the parameter f may depend on the numerical aperture of the illuminator IL. Additionally or alternatively, the parameter f may depend on the spectrum of the vibration of the illuminator IL.

Figures 2 and 3 show the results of a simulation of the tristimulus dose change (in units of reduction) as a function of the frequency of the vibration caused by the vibration of the illuminator IL relative to the frame MF. The change in the three sigma dose in the reduced unit is defined as the ratio of the amplitude of the triple sigma dose (as a percentage) to the amplitude of the slit SL vibration (in arbitrary length units). The triple sigma dose change is defined as the ratio of three times the standard deviation of the dose to the average dose. Figure 3 is an enlarged section of the graph of Figure 2, shown on a smaller scale.

The first curve 210 illustrates the dose change when no correction is made for the relative movement of the illuminator IL and the frame MF. Curve 210 oscillates with a plurality of periodic alternating maximums 211 and 212. The minimum value 212 corresponds to the vibration frequency at which the exposure time of the substrate W (i.e., the time it takes for the radiation band to pass through each point on the substrate) is approximately equal to an integer number of cycles of the vibration. In addition, the magnitude of the periodic maximum 211 decreases as the vibration frequency increases.

The second curve 220 illustrates the dose change multiplied by a factor of 200 when the correction based on equation (2) is made for the relative movement of the illuminator IL and the frame MF (so that it is clearly visible on the same scale as the curve 210). Curve 220 also oscillates and has a plurality of periodic alternating maximums 221 and minimums 222. The magnitude of the periodic maximum 221 is substantially the same.

The third curve 230 illustrates the dose change multiplied by a factor of 200 when the correction based on equation (6) is made for the relative movement of the illuminator IL and the frame MF (so that it is clearly visible on the same scale as the curve 210), where the parameter f =0.994. Curve 230 also oscillates and has a plurality of periodic alternating maximums 231 and minimums 232. The magnitude of the periodic maximum 231 oscillates as the vibration frequency increases.

All three curves 210, 220, 230 correspond to the condition that all of the fingers of the illuminator IL are completely contracted from the path of the radiation beam PB. Figure 2 illustrates the reduction of a factor of about 100 for the total scale of the three sigma dose changes, at least for relatively low frequencies, by applying a correction based on equation (2). Additionally, for relatively low frequencies, an additional (relatively small) reduction in tristimulus dose variation can be achieved by applying a correction based on equation (6) (where f = 0.994). At higher frequencies, the reduction in the three sigma dose changes in units of reduction is achieved by applying a correction based on equation (6) (where f = 0.994) to the reduction achieved by applying the correction based on equation (2). Due to the nature of the coupling between the illuminator IL and the frame MF, one can expect that any induced vibration of the illuminator IL is at a relatively low frequency.

Figure 4 shows the variation of the three sigma dose caused by the vibration of the illuminator IL relative to the frame MF caused by the vibration of the illuminator IL relative to the frame MF when the finger of the illuminator IL is partially inserted into the path of the radiation beam PB (to be reduced) The result of the simulation of the unit). In particular, the fingers are inserted into the path of the radiation beam PB to achieve an attenuation of about 10% of the radiation beam PB. The first curve 310 illustrates the dose change when the relative movement of the illuminator IL and the frame MF is not corrected, and the second curve 320 illustrates the dose change multiplied by a factor of 25 when performing the correction based on equation (2) (so that it is It is apparent on the same scale as curve 310, and the third curve 330 illustrates the dose change multiplied by a factor of 25 when making a correction based on equation (6) (so that it is clearly visible on the same scale as curve 210), wherein The parameter f = 0.994.

Figure 4 illustrates that in the case where the fingers of the illuminator IL are inserted to obtain an attenuation of about 10%, by applying the correction based on equation (2), there is a total scale of the variation of the three sigma doses in units of reduction. The reduction, the reduction factor increases as the vibration frequency increases. In addition, in the case where the finger of the illuminator IL is inserted to obtain an attenuation of about 10%, there is no actual gain obtained by applying the correction based on the correction of equation (6) (where f = 0.994). Therefore, there is almost no advantage in using parameterization with f different from one. However, it should be noted that approximately 10% of the attenuation of the fingers is extremely high. In practice, less than 10% attenuation can be used, and in general, the level of attenuation will vary along the length of the slot SL of the illuminator IL.

A mechanism for adjusting the energy or power of each pulse of a pulsed laser beam output by a laser will now be described.

Energy is supplied to the radiation source SO. For example, for embodiments where the radiation source is laser, energy can be supplied to the laser gain medium by an external source. This procedure is referred to as twitching and the external source may include: electrical power supply (electric twitching), electromagnetic radiation (optical twitching), airflow (gas dynamic twitching), or some other suitable energy source. The external power source can be adjusted such that the amount of pumping power supplied to the gain medium can vary. The external power source can be provided with one or more input variables that can be varied to vary the power supplied to the gain medium. For example, in the case of a gas laser such as a quasi-molecular laser, the external power source can include a pair of discharge conductors across which a high voltage is applied. For such embodiments, the power supplied to the gain medium can be varied by varying the voltage applied across the conductor. In the case of a gas discharge lamp such as a mercury lamp, the external power source can include a pair of main electrodes that are applied across the pair of main electrodes to establish and maintain an arc. For such embodiments, the power supplied to the gain medium can be varied by varying the voltage applied across the main electrode.

In general, the power of the laser beam will depend on the pumping power supplied by the external power source. If one or more variables of the external power supply (eg, a high voltage applied across a pair of discharge conductors) is known to the power of the beam, the values of the variables can be selected accordingly. To achieve the required power. The relationship can be parameterized as a polynomial having one or more free parameters that can be determined during the calibration procedure. Moreover, the relationship may change over time and, therefore, may need to be performed periodically calibration.

For example, in the case of excimer lasers, the power of the laser is dependent on the high voltage V applied across the two conductors. In general, this relationship is non-linear. However, for the range of the voltage V used in practice, the power P of the laser can be well approximated by the polynomial expansion of the voltage V. For a sufficiently small range of voltage V , the relationship between power P and voltage can be approximated by the following linear relationship: P = O + G × V , (7) where the laser gain G and offset O are available in the calibration procedure The parameters determined during the period. For larger ranges of voltages, higher order polynomials with more tunable parameters may be necessary to parameterize the relationship between voltage V and power P.

In practice, the output power P of the radiation source SO (eg, as measured by a radiation sensor) will include elements of noise. Thus, the calibration procedure can use data from long periods of time to evaluate parameters for the relationship between one or more variables and power of the external power supply. The value of the parameter can drift over time as the lithographic apparatus operates, and thus, the calibration procedure can be used to periodically determine the parameters.

The power P can be measured by the radiation sensor RS. The radiation sensor RS can be any sensor suitable for measuring the radiant energy incident on the radiation sensor RS. For example, the radiation sensor RS can be a photodiode. The radiation sensor RS can be positioned such that at least a portion of the radiation beam produced by the radiation source SO is incident on the radiation sensor RS. For embodiments in which only a portion of the radiation beam generated by the radiation source SO is incident on the radiation sensor RS, the relationship between the dose received by the radiation sensor RS and the dose received by the substrate W should be known to us. This makes it possible to determine the latter from the measurement of the former.

An example location of the radiation sensor RS is depicted in FIG. The partially transmissive mirror 100 is positioned in the illuminator IL. The partially transmissive mirror 100 reflects the first portion 101 of the radiation beam onto the radiation sensor RS. The remaining portion 102 of the radiation beam is transmitted by the partially transmissive mirror 100 and transmitted to the patterning device MA. The fraction of the radiation beam reflected by the partially transmissive mirror 100 (The first portion 101) can be, for example, about a few percent or less of the radiation beam. If this fraction is known to us, the measurement by the radiation sensor RS can be used to calculate the energy of the radiation beam 102 transmitted by the partially transmissive mirror 100. If the fraction is not known to us, a second radiation sensor (not shown) can be used, by replacing the substrate with the second radiation sensor and comparing the measurement by two radiation sensors. The energy is used to calibrate the radiation sensor RS.

In other embodiments, the partially transmissive mirror 100 and the radiation sensor RS can be located at other locations along the path of the radiation beam. For example, the partially transmissive mirror 100 and the radiation sensor RS can be positioned before the illuminator IL (eg, in a beam delivery system).

Embodiments of the present invention are operable to control the power of the radiation beam depending on the number of speeds indicative of the radiation system relative to the frame to reduce variations in the amount of energy received by the substrate caused by the relative motion of the radiation system and the frame. Thus, the change in the dose of energy received by the substrate caused by the relative motion of the radiation system and the frame is at least partially corrected.

Although the above embodiment uses an accelerometer AC mounted on the illuminator IL to determine the instantaneous velocity of the slot SL in the scanning direction, other mechanisms operable to determine the amount of speed indicative of the illuminator relative to the frame may alternatively be used. For example, one such mechanism may include a camera mounted on a frame MF that is operable to directly measure movement of the radiation belt relative to the frame MF.

The power of the radiation beam is the rate at which it supplies energy. Power has energy units per unit time (eg, W). The irradiance of the radiation beam incident on the surface is the power of the radiation beam incident on the surface per unit area. The irradiance has an energy unit per unit area per unit time (for example, Wm ^-2 ). In the above-mentioned invention, the terms "power" and "irradiance" are used interchangeably, and the context of the content from the use is clear.

In the above invention, the amount of energy received by the substrate W per unit area may be referred to interchangeably as "radiation dose", "energy dose", "energy dose" or "dose".

Although the radiation source SO has been described as containing a laser, the radiation source SO may be a radiation source SO Any form. For example, the radiation source SO can be an EUV radiation source (eg, a discharge-generating plasma source, a laser-generated plasma source, or a free-electron laser) or a lamp-type source (eg, a mercury discharge lamp).

Although the embodiments of the present invention have been described above in the context of the DUV lithography apparatus using transmissive optics, embodiments of the present invention are also applicable to EUV lithography apparatus using reflective optics.

Although the specific embodiments of the invention have been described above, it is understood that the invention may be practiced otherwise than as described. This description is not intended to limit the invention.

210‧‧‧First curve

211‧‧‧ periodic maximum

220‧‧‧second curve

221‧‧‧Periodic maximum

222‧‧‧min

230‧‧‧ third curve

231‧‧‧Periodic maximum

232‧‧‧min

Claims (20)

A lithography apparatus comprising: a radiation system operable to generate a radiation beam; a frame; a substrate stage for holding a substrate, the substrate stage being movably mounted to The frame is configured such that a target portion of the substrate is configured to receive the radiation beam; a scanning mechanism operative to move the substrate table relative to the frame; and a mechanism operable to Determining the speed of the radiation system in a scan direction and in a plane of the substrate relative to the frame; wherein the radiation system is provided with an adjustment mechanism operable to control the power of one of the radiation beams such that Equal to a base power multiplied by a factor that is related to the scanning speed of the substrate table relative to the frame and the velocity of the radiation system relative to the frame in the scanning direction and in the plane of the substrate A vector sum is proportional to a change in one of the doses of radiation received by the substrate caused by the relative motion of the radiation system and the frame. A lithography apparatus as claimed in claim 1, wherein the mechanism operable to determine the speed of the radiation system relative to the frame comprises one or more accelerometers mounted on the radiation system. The lithography apparatus of claim 1 or 2, wherein the mechanism operable to determine the speed of the radiation system relative to the frame comprises one or more cameras mounted on the frame, the one or more cameras Operation is to measure the movement of a radiation band that emits one of the radiation systems. The lithography apparatus of claim 1 or 2, wherein the factor comprises one or more tunable parameters number. The lithography apparatus of claim 4, wherein the factor is proportional to a vector sum of one of: a scanning speed of the substrate stage relative to one of the frames; and a parameter f and the radiation beam are in a scanning direction A product of the plane of the substrate relative to one of the speeds of the frame. The lithography apparatus of claim 1 or 2, wherein the factor is a ratio of the sum to the scanning speed of the substrate table relative to the frame. A lithography apparatus according to claim 1 or 2, wherein the radiation system comprises a radiation source operable to generate a radiation beam, and an illumination system operable to adjust the radiation beam. The lithography apparatus of claim 1 or 2, wherein the radiation system comprises an exit slot and the velocity of the radiation system in the scanning direction and in the plane of the substrate relative to the frame is equal to a velocity of the exit slot . The lithography apparatus of claim 1 or 2, further comprising a support structure for supporting a patterned device, wherein the radiation system is configured to project the radiation beam onto the patterned device such that the patterned device A pattern is imparted in the cross section of the radiation beam before the radiation beam is received by the target portion of the substrate. The lithography apparatus of claim 9, wherein the support structure is movably mounted to the frame, and wherein the scanning mechanism is further operative to move the support structure relative to the frame. The lithography apparatus of claim 1 or 2, further comprising a projection system for projecting the radiation beam as a radiation strip onto the target portion of the substrate. The lithography apparatus of claim 11, wherein the projection system is coupled to the frame. The lithography apparatus of claim 1 or 2, wherein the radiation system comprises a laser. A method comprising: providing a substrate; providing a radiation beam using a radiation system; using a patterning device to impart a pattern to the radiation beam in a cross section of the radiation beam; Projecting a radiation beam onto a target portion of the substrate; using a scanning mechanism to move the substrate relative to a frame such that the patterned radiation beam moves over a surface of the substrate; determining that the radiation system is the scan direction and a plane of the substrate at a relative speed of one of the frame; and one of the control power of the radiation beam, such that it is substantially equal to a power multiplied by a factor, the factor and the substrate table relative to the frame One of the scanning speeds is proportional to a vector sum of the radiation system in the scanning direction and in the plane of the substrate relative to the velocity of the frame to reduce the relative motion caused by the relative motion of the radiation system and the frame One of the doses of radiation received by the substrate varies. A method comprising: receiving a radiation system in a scanning direction and in a plane of the substrate relative to a speed of a frame; and providing an instruction to a radiation source, the instructions for controlling the radiation source Outputting a power of one of the radiation beams such that it is equal to a base power multiplied by a factor that is proportional to the scanning speed of the substrate table relative to the frame and the radiation system in the scanning direction and in the plane of the substrate A vector sum of the velocity relative to the frame is proportional to reduce a change in one of the doses of radiation received by one of the substrates relative to the frame caused by the relative motion of the radiation system and the frame. The method of claim 15, wherein the velocity of the radiation system relative to the frame is an acceleration of the radiation system in a scanning direction, and the method includes a solution The acceleration is integrated in the resolution time to calculate a step of the average speed of the radiation system in the scanning direction during the resolution time. The method of claim 15 or 16, wherein the factor comprises one or more tunable parameters. The method of claim 17, wherein the factor is proportional to a vector sum of one of: a scanning speed of the substrate relative to the frame; and a parameter f and the radiation beam in the scanning direction on the substrate The product of the plane relative to one of the speeds of the frame. The method of claim 15 or 16, wherein the factor is a ratio of the sum to the scanning speed of the substrate table relative to the frame. A computer program operable to implement the method of any one of claims 15 to 19.